An Improvement of Hölder Integral Inequality on Fractal Sets and Some Related Simpson-Like Inequalities

Abstract

The purpose of this work is to investigate some inequalities for generalized [Formula: see text]-convexity on fractal sets [Formula: see text], which are associated with Simpson-like inequalities. To this end, an improved version of Hölder inequality and a Simpson-like identity on fractal sets are established, in view of which we give several estimation-type results involving Simpson-like inequalities for the first-order differentiable mappings. Moreover, we provide five examples to illustrate our results. As applications with respect to local fractional integrals, we derive two inequalities according to [Formula: see text]-type special means and generalized probability density functions.

Error bounds on the Hermite-Hadamard- and Bullen-type inequalities for $2\alpha$-local fractional derivative

“…After that, some generalized Milne-type integral inequalities for generalized m-convexity are achieved, which are further supported by several examples and applications in [5]. For more research results on local fractional calculus, please consult the papers [6,23,25,32] and the references therein.…”

Some Hermite–Hadamard type inequalities for GA‐s‐convex functions in the fourth sense

“…The basic structures of this theory are convex sets and convex functions, which play a crucial role in the advancement and applications of it in various branches of applied and pure mathematics 1–7 . Due to the widespread use of convexity in modern analysis, the notion of convex functions has been extended and generalized in several directions 8–19 . Some of these generalizations modify the domain or range of the function while preserving the basic structure of a convex function as it is defined in Peajcariaac and Tong 20 as follows:…”

“…[1][2][3][4][5][6][7] Due to the widespread use of convexity in modern analysis, the notion of convex functions has been extended and generalized in several directions. [8][9][10][11][12][13][14][15][16][17][18][19] Some of these generalizations modify the domain or range of the function while preserving the basic structure of a convex function as it is defined in Peajcariaac and Tong 20…”